Trace Formulas in Higher Dimensions

ABSTRACT The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self‐adjoint and maximal dissipative operators. They cover both ideals with normal and singular traces. The admissible function classes considered in the trace formulas include both analytic and nonanalytic scalar functions. Results are illustrated with examples.